Help please : Poor battery life in note 3

1. i am a galaxy note 3 (N900,Dec 2013 model) user from India. I had bought this phone from my cousin post 5 months of usage. As a whole the phone is great and I am happy with it. my problem is that I am getting very poor battery backup. with full charge and moderate use , I am getting a backup of 16-17 hours average with a screen time of 4 to 5 hours. Please note that I use the phone mainly for browsing the net ,whatsapp and calls for less than an hour daily. As 3G or WDMA drains my battery swiftly i have put it on GSM only. Guys ,do everyone get the same backup ? Especially those who are having phones 8 months or more old ?? And its worth mentioning that i put my screen on auto brightness (mostly in low mode ), has disabled gestures and wifi ,gps are always off.i have tried the power saving mode and there is no much difference.i clear the background applications regularly, but still more than 2 GB of my ram will always be in use. sometimes i feel my phone is getting heated,especially when i keep it on my ears when making calls. I still have 4 months of warranty remaining , is there really any problem with my phone or is it the battery who is the villain?? Please help me. your assistance will be greatly appreciated.

2. I also hear a mild noise running in the background when making calls , is this a problem with the phone or network ?

Should i ROOT my phone ? will it do any good regarding the battery life ?? what all are the pros and cons of rooting

cheers
Dr Heart

PS: i opted for note 3 for its battery and its the thing that i am getting the least now

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